Two formulations are proposed to filter out correlations in the residuals of the multivariate GARCH model. The first approach is to estimate the correlation matrix as a parameter and transform any joint distribution to have an arbitrary correlation matrix. The second approach transforms time series data into an uncorrelated residual based on the eigenvalue decomposition of a correlation matrix. The empirical performance of these methods is examined through a prediction task for foreign exchange rates and compared with other methodologies in terms of the out-of-sample likelihood. By using these approaches, the DCC-GARCH residual can be almost independent.
This paper presents a new approximation method for pricing multi-asset continuous single-barrier options. Barrier options are frequently traded, and it is necessary for practitioners to evaluate these precisely and quickly, both for competitiveness, and for risk management. However, it is a difficult task under local stochastic volatility models. To the best of our knowledge, this paper is the first to provide an analytical approximation for continuous barrier options prices in a multi-asset environment. In numerical experiments, we examine the validity of the formula by using parameters calibrated to EURUSD European options.
This paper proposes a new approximation method for pricing barrier options with discrete monitoring under stochastic volatility environment. In particular, the integration-by-parts formula and the duality formula in Malliavin calculus are effectively applied in an asymptotic expansion approach. First, the paper derives an asymptotic expansion for generalized Wiener functionals. After it is applied to pricing path-dependent derivatives with discrete monitoring, the paper presents an analytic (approximation) formula for valuation of discrete barrier options under stochastic volatility environment. To our knowledge, this paper is the first one that shows an analytical approximation for pricing discrete barrier options with stochastic volatility models. Finally, it provides numerical examples for pricing double barrier call options with discrete monitoring under the Heston model.
This online appendix provides results omitted in the paper with the same title. Appendix A explains all the definitions and equations necessary for practical computations of an option pricing formula in Theorem 4.3: Section A.1 gives a summary with Corollary A.1, which shows our pricing formula with complete expressions of constants Ci,k (i = 1, 2, 3), Cj (j = 4, 5, 6) appearing in the theorem. Section A.2. provides the details of the derivation. Appendix B lists up the conditional expectation formulas used in the derivation of the theorem.
This paper shows the relationship between the forward start volatility swap price and the forward start zero vanna implied volatility of forward start options in rough volatility models. It is shown that in the short time-to-maturity limit the approximation error in the leading term of the correlated case with $H\in(0,\frac12)$ does not depend on the time to forward start date, but only on the difference between the maturity date and forward start date and on the Hurst parameter $H$.
Black (1976) advocated the idea of trading commodities as 'equities without dividends' and made use of geometric Brownian motion. However, given the complexity of the shapes associated with the term structure of commodities futures, the simple geometric Brownian motion model proposed by Black (1976) is not a good t. To resolve this problem, mean reversion has been introduced. Unlike equities, when commodities prices rise, there is generally (albeit with a time lag) an increase in supply; conversely, when prices decline, supply decreases. e fact that prices are determined by the supply and demand balance means that the supply side adjusts supply volumes, which has the eect of constraining the potential for commodities prices to move in a single direction. at is why it is generally considered appropriate to employ mean reversion in commodity pricing models. Much empirical research has been carried out on this subject. For example, it was veried by Bessembinder et al. (1995).
For a general stochastic volatility framework with non-zero correlation between the spot price and the instantaneous volatility, an analytical approximation for single barrier options with continuous monitoring is given. The approximation is expressed only in terms of market observable implied volatilities and prices. As such the approximation is independent of the specific form and number of parameters of the skew-generating stochastic volatility model.
This paper presents a new approximation method for pricing multi-asset continuous single barrier options under general local stochastic volatility models. The formula applies an asymptotic expansion technique and an approximation for the distribution of the first exit time of diffusion processes. This method focuses on local stochastic volatility models with unknown characteristic function and transition density function. To the best of our knowledge, our approximation formula is the first to achieve analytic approximations for continuous barrier options prices in this environment. In numerical experiments, we confirm the validity of the formula.
